authors: Mykola Chumak, Vasyl` Yefymenko
Urgency of the research. The main task of both the foundations and the philosophy of physics is the analysis and restructuring of physical theories that should begin with the characterization of physical theory in the most general terms. At first glance, this task is not particularly difficult. First, there is nothing in physical theory but mathematical formalism, provided by physical interpretation and capable of coexistence with other theories and which can be verified by experiment. It looks beautiful and sounds simple, but it's actually a tricky thing to do.
Target setting. What are the assumptions and theorems of this physical theory, if it is taken for granted, are they just mathematical theorems or something else? - Do the key formulas that we want to systematize determine the formalism of physical theory in a single way, or are there alternatives, and if so, are they equivalent in all respects? These are just a few of the many questions posed by the very notion of physical theory. The depth and acuteness of each of them are such that many of them can not be answered otherwise than as a fundamental article or even a whole book. All this confirms the general rule: what is obvious to the practice of science can be problematic for its philosopher. Since we cannot deal with every possible problem of the fundamentals of physics and every philosophical problem connected with physical theories in general, we shall choose to consider only a few of them.
Actual scientific researches and issues analysis. The movement from classical physics to modern physics occurred as a result of the emergence of a number of paradoxes in classical theory. This feature is characteristic to some extent of the electromagnetic theory of Maxwell, Einstein's theory of relativity, etc.
The research objective. We will try to consider the key terms of physical theory and show the role of the mathematical component in its creation.
The statement of basic materials. The article deals with some modern problems of the methodology and foundations of physics, in particular: whether mathematical formalisms contain interpretations of themselves or whether they need to be supplemented by interpretive predictions, and if so, how these predictions are formulated; what physical theories describe: physical systems or laboratory operations, either one or another, or neither of them; how the basic concepts of theory should be introduced, by reference to measuring operations, or by means of clear definitions, or axiomatically; how physical theories relate to each other; how theory relates to experiment: directly or with the help of additional theories.
Conclusions. In modern philosophical, mathematical and natural-scientific languages, theory is understood not just as a random thought, but as a hypotheticaldeductive system, that is, a set of formulas generated by logic and mathematics by a group of initial assumptions. Because of the commonality of some of these initial assumptions, as well as the possibilities for transformation provided by logic and mathematics, each theory is some infinite set of formulas. The role of mathematics in modern science is twofold: the formation of concepts and computation. There is no instantaneous velocity without derivative, no law of motion without differential or operator equations. Mathematical concepts are not only convenient aids, but they are also the very essence of physical ideas. And a simple prophecy of the future state of the system or the probability of this or that event would be impossible without the deductive power of the internally present formalism of the theory. This deductive force is so striking that we often tend to equate theoretical physics with computation, forgetting the role of mathematicians in the very formation of physical concepts, formulas, and theories.
Keywords: physical theory, basic terms of physical theory, mathematical component of the theory.
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